In a tiny Mexican coastal village, the fisherman had long been given up for dead. Lost at sea more than a year ago, in terrible conditions that claimed the lives of four others, there was no hope of his return.

So it was with a mixture of astonishment and jubilation that the boatmen of Costa Azul, a picturesque hamlet in the southern Chiapas region, received news that one of their number had apparently turned up more than 12,000 kilometres away in the Marshall Islands.

Don’t you believe in miracles?

Jose Salvador Alvarenga’s astonishing tale of survival in a seven-metre fibreglass vessel has met with disbelief in some quarters. Doctors expressed surprise at his relative good health. His tale of surviving on fish, sharks, turtles and the blood of birds caught by hand seemed too fantastic to some.

But in Costa Azul, there were tears as fishermen saw on television the image of the man they called “La Chancha,” an affectionate name for someone of large girth.

“It’s him. He worked for me for a year and I’ve known him for 10 years,” said Bellarmino Rodriguez Solis, 64, who claimed to own the boat Mr Alvarenga was in. When The Daily Telegraph showed him a photograph of the boat, beached in the Marshall islands, he cried: “It’s my boat, it’s my boat. I know the number on the side.”

Through tears, he added: “Don’t you believe in miracles? It’s a miracle. When we saw it on TV all the fishermen were shouting and jumping up and down. We couldn’t believe it was La Chancha. I hope he comes back here. We’re desperate to see him and throw a big party. We will kill a cow and we will drink beer and tequila and eat fish.”

Mr Solis could not produce any paperwork to show that he owned the boat. But standing next to a small jetty, where they said Mr Alvarenga set off from, a series of fishermen described the day they said he was lost.

They said four people were presumed to have died in two other boats that were never heard from again, amid high winds and towering waves.

They did not agree on the date of the disappearance. Mr Solis gave it as Nov 17, 2012 but several other fishermen said Dec 17, 2012. None of them had paperwork to verify the date.

Fisherman Jose Alfredo Diaz Hill, 25, said he was out in the storm with Mr Alvarenga and was the last person to see him before he was lost.

He said: “I passed by his boat at 2.30 p.m. and he said he would radio me at 4 p.m. but he never called. Later, I heard he never came back. Everyone thought he was dead. You can’t come back from that storm, it’s impossible.

It was very difficult for the rest of us to get back. We thanked God that we were alive.”

Hector Arebalo Castellonos, 22, said: “He said on the radio he had lost all his equipment. He sounded desperate. He sounded like he was crying but there was nothing we could do. We couldn’t get back out again for three days because of high winds and high waves.

“After that we searched for five days, and for a month if we saw a light we would go out to see if anyone was there.”

Jorge Cisneros, 51, said: “There was no chance of finding them. The waves were eight to 10 metres high.

“It’s a dangerous business. You know you’re going out to fish but you never know if you’re going to come back. If we had gone out there to find him we would have all been dead.”

Mr Solis said: “I spoke to him on the radio at midday the day after he went out. He said ’The boat’s broken.’ He had some co-ordinates but he wasn’t sure how far out he was. I told him ’We are sending people for you’. He was really brave. He had hope we could find him. He was swearing.”

The first photographs of the boat in which Mr Alvarenga made his long trip were obtained by The Daily Telegraph Tuesday.

They showed a small, heavily-damaged fibreglass vessel with a broken motor. About seven metres long, it was empty aside from a blue container in which Mr Alvarenga would hide, to seek shelter from the sun, and in normal circumstances, store his catch. It was emblazoned with the name Camaroneros de la Costa, the fishing cooperative for which Mr Alvarenga worked in Mexico. Dozens of mussels were attached to the hull, suggesting the vessel had drifted slowly.

The boat remains on Ebon atoll, a barely-populated outlying cluster of islands in the Marshalls, where the police have inspected it and took the photographs. Mr Alvarenga was brought by boat to the capital, Majuro, on Monday, and has now been transferred from a hospital to a hotel.

He broke down in tears yesterday as he spoke to his parents and 14-year-old daughter, Fatima, who live in a small fishing village in El Salvador, and to his brothers, who live in the United States. Later he received a lengthy haircut to his shaggy locks and bushy beard.

His parents, Jose Ricardo Orellana and Maria Julia Alvarenga, told El Salvador’s El Mundo newspaper of their delight at their son’s “incredible” survival, which they had prayed for over and over.

They had not seen Mr Alvarenga in some years and proudly showed pictures of him, appearing younger.

Fatima appeared shy but said: “First thing I’ll do is to hug him and kiss him.”

His mother said she dreamt of her son’s survival and hoped he would soon return home.

I saw him alive in my dreams

“I dreamed about him, I saw him alive in my dreams, but then he vanished.”

Mexican officials are due to arrive in the Marshall Islands today to speak to Mr Alvarenga. They are hoping to return him to his home town, and to investigate the death of Ezekiel, a 15-year-old who he said had been on the boat with him.

Authorities are still trying to verify Mr Alvarenga’s account.

“I don’t know whether he is telling us the truth until we get the facts from his fingerprints and everything,” George Lanwi, commissioner of the Marshall Islands police force, told The Telegraph.

In small corners of Mexico and El Salvador, there is, however, no doubt.